Developments in diffractive optics technology have opened the doors for diffractive optical elements ("DOEs") to play major roles in a wide number of optical systems and applications including high resolution imaging systems such as head-mounted displays, focussing and collimating optics for fiber-optic couplers and connectors and other optical interconnect applications, and chromatic aberration correction of refractive optical elements.
One type of diffractive optical element known as a "natural hologram" is fabricated by creating interference among coherent light beams on a photographic plate and then developing the photographic plate. An example of such a hologram may be seen in U.S. Pat. No. 4,607,914 by Fienup titled "Optical System Design Techniques Using Holographic Optical Element." These natural holograms, however, are difficult to mass produce.
In order to overcome the mass production problems with interferometric holograms, computer generated holograms ("CGHs") have been developed. CGHs have been fabricated by calculating the desired holographic pattern to perform a particular function and then forming the pattern on a glass or other substrate using photolithographic or other techniques. This technique is described, for example, in U.S. Pat. No. 4,960,311 by Moss et al. titled "Holographic Exposure System For Computer Generated Holograms."
When natural holograms are used to replace conventional refractive optical elements such as lenses and prisms, they are typically referred to as holographic optical elements ("HOEs"). In order to distinguish HOEs from CGHs when CGHs are used to replace similar refractive elements, they are typically referred to as diffractive optical elements ("DOEs").
While natural holograms are conventionally analog in nature, CGHs on the other hand are conventionally digital in nature. That is the calculation of the CGH is often done by calculating a CGH pattern at discrete locations often referred to as "pixels" and quantizing phase and/or amplitude functions to discrete levels. This is done principally to simplify the fabrication of CGHs. For example, in U.S. Pat. No. 4,895,790 by Swanson et al. titled "High-Efficiency, Multilevel, Diffractive Optical Elements," a method is described for fabricating CGHs containing 2.sup.N phase levels, where N is the number of masks and etching steps employed.
DOEs, however, can also be fabricated by a continuous method, for example by diamond turning the calculated pattern onto a glass substrate. DOEs fabricated in this manner are often termed continuous DOEs, while DOEs fabricated with discrete steps are typically termed, "binary optics," "multilevel DOEs", or "digital optics."
A well known problem associated with DOEs is a large amount of chromatic aberrations. For example, while a single DOE can be designed to yield diffraction limited performance for imaging or focussing a single wavelength, the DOE exhibits severe chromatic aberrations, much larger than that of a comparable refractive imaging/focusing lens, when wavelengths other than the design wavelength are employed.
This is especially important when a broadband light source, such as an LED, is used (e.g., for imaging, collimating, or focussing) with a DOE. It is also important, however, when a very narrow band light source such as a laser diode is employed. This is because the lasing wavelength of laser diodes typically has a very high sensitivity to temperature, e.g., 0.30-0.5 nanometers per degree centigrade (.degree.C.). In addition, many fiber-optic connectors are designed to operate with several different types of laser diodes, each having a different wavelength.
While it is known that a refractive optical element can be combined with a DOE to perform achromatic imaging, it is much more difficult to achieve achromatic imaging with solely diffractive elements. Due to their low cost, it is often desirable to manufacture DOEs with solely diffractive surfaces, especially in large volumes.
It is also known that two DOEs can be analytically designed or designed with computer ray tracing procedures so that they function together to reduce chromatic aberrations. For example, in a publication titled "Wavelength Independent Grating Lens System," Applied Optics, Vol. 28, No. 4, pp. 682-686, 1989, by Kato et al., a method was described having two distinct DOEs in a complimentary manner so that two different wavelengths could be brought to a common focal point. A ray tracing procedure is described in which two holograms are used to image a point on-axis. The spatial frequency at each point along the radius (r) of each DOE is calculated so that rays for two different wavelengths are brought to a common focus. The DOE is then fabricated with a grating period that varies as a function of r. The period of the grating as a function of r is determined by the spatial frequencies calculated during the ray tracing procedure.
This particular technique, however, has several drawbacks. First, the diffraction efficiency of this technique is severely limited. The gratings employed are binary gratings. Binary phase gratings have an efficiency of about 40% for a combined efficiency of about 16% for transmission through both DOEs.
The number of levels that can be employed with such a technique is limited by the minimum feature size of such processes. The maximum number of phase levels (N) that can be employed in such a process is given by: EQU N.ltoreq.T/.delta. (1)
where delta (.delta.) is the minimum feature size. The diffraction efficiency (.eta.) in the +1 order of a grating with N phase levels is given by Equation (2) set forth below: ##EQU1##
If the grating period needed is 2 micrometers (.mu.m) and the minimum feature size is 0.5 .mu.m, then the maximum number of phase levels that can be employed is 4, yielding an efficiency of each DOE of about 80% and combined efficiency of about 64%. Note that this limitation stems from a design procedure that considers only a single diffraction order emanating from each grating (the +1 order), when in actuality, for a multilevel DOE, multiple orders are actually generated.
This limitation is a drawback of ray tracing and continuous analytic techniques. That is, the DOE surfaces are modelled as continuous functions or continuous blazed gratings. Such continuous functions/gratings generate only a +1 order with 100% efficiency (in theory). In practice, a multilevel DOE is not continuous. The discrete steps are responsible for generating multiple diffraction orders, lowering the efficiency in the +1 diffraction order.
A second drawback of this approach is that the two optical elements must be placed relatively far apart to minimize the spatial frequencies contained in the elements. The maximum deflection angle that can be realized with reasonable diffraction efficiency with state-of-the-art fabrication techniques is approximately 25 degrees (.degree.). Assuming a source divergence half angle of 15.degree. and equal sized elements, this limits the distance (D) of separation between the two DOEs to greater than about three times the diameter (d) of each of the elements. In many cases, it is desirable to place the elements closer together to improve alignability or reduce the overall system volume.
A third drawback is that this approach is not a diffraction based approach, but instead a geometrical optics based approach. Thus, while it can be used to minimize or eliminate geometrical aberrations, it will not in most cases achieve diffraction limited performance. That is the optimization procedure will result in perfect geometrical optics performance for two different wavelengths, but no diffraction effects are accounted for in this procedure. Thus, the tailoring of the side lobes of the DOE and other diffraction based effects cannot be performed with this procedure. Thus, for example, it could not be used directly to optimize the coupling efficiency for a laser-to-fiber coupler or to create a flat-top profile.
Fourth, this method is limited to radially symmetric DOEs. This is a drawback for use with many commercial diode lasers that contain different divergence angles in the two orthogonal directions. For such asymmetrical cases, it is often desirable to have non-radially symmetric anamorphic lenses.
Finally, with this method, the resulting DOEs are generally not identical to each other. In some cases, as in separable fiber-optic couplers, it is desirable to have the two DOEs identical so that the parts can be interchangeable as with conventional fiber-optic separable connectors.
Another method that is known for designing DOEs is iterative encoding methods such as iterative discrete on-axis ("IDO") encoding described in the publication titled "Iterative Encoding Of High-Efficiency Holograms For Generation Of Spot Arrays," Optical Society of America, pp. 479-81, 1989, by co-inventor Feldman et al., and radially symmetric iterative discrete on-axis ("RSIDO") encoding described in U.S. Pat. No. 5,202,775 titled "Radially Symmetric Hologram And Method Of Fabricating The Same" also by co-inventor Feldman et al.
In the IDO encoding method, the DOE is divided into a two-dimensional array of rectangular cells. An initial transmittance value for each rectangular cell is chosen. An iterative optimization process, such as simulated annealing, is then used to optimize the transmittance values of the cells. This is achieved by choosing an error function for the hologram that is a measure of the image quality. A single cell is changed, and the change in the output pattern is computed. The error function is then recalculated. Based upon the change in the error function, the change is either accepted or rejected. The process is iteratively repeated until an acceptable value of the error function is reached which optimizes the image quality. Computers are often used for performing these iterations because of the immense time involved in the optical system calculations.
The RSIDO encoding method is another iterative method, except that the cells are radial rings rather than rectangular and not only are the phase values of each cell optimized, but also the transition points. Although this method has been shown to be successful for various applications, the amount of chromatic compensation that can be achieved with this method, however, may be limited.
Another known method for designing DOEs for achromatic operation, such as described in the publications titled "Deep Three-dimensional Microstructure Fabrication For IR Binary Optics," J. Vac. Sci. Technol. B10, pp. 2520-2525, 1992 by Stern et al. and titled "Dry Etching: Path To Coherent Refractive Microlens Arrays," SPIE Proc., pp. 283-292, 1992, is to create deep multilevel DOEs that have phase depths that are larger than conventional multilevel DOEs. In conventional digital optics, the phase depth (d.sub.m) of each level is given by ##EQU2## where n is the index of refraction and m=0, 1, . . . N-1 and .lambda. is the central wavelength. This will result in a phase difference between the m=0 level and any other level of 2.pi. m/N.
In a deep multilevel DOE, on the other hand, the phase difference is set equal to an integer number multiple of 2.pi. (m/N) (e.g., 4.pi. m/N or 6.pi. m/N). It is known that d.sub.m can be set equal to any integer multiple of 2.pi. and the DOE will not function any differently. Within predetermined paraxial approximations at the design wavelength, however, the chromatic aberrations about this wavelength will improve.
A problem with this approach is that the diffraction efficiency is less than that of the conventional DOE approach. Instead of Equation 2, the diffraction efficiency for the deep multilevel approach is: ##EQU3## where p is the integer multiple of 2.pi. employed. Thus, for example if the phase difference were set to 8.pi.m/N, p would have a value of 4, and for an 8 phase level structure, the diffraction efficiency of a deep multilevel DOE would be only 40% as compared to 95% for an 8 phase level conventional multilevel DOE.
In practice, the above approaches have resulted in reasonable efficiency DOEs with only a small amount of chromatic aberration for practical applications. For example, for laser diode-to-fiber couplers, a coupling efficiency of greater than 70% was achievable with a single wavelength. Over an operating temperature range of -40.degree. to +85.degree. C., however, less than about 5% may be achieved with a single DOE designed with commercial ray tracing programs. By using a single element RSIDO encoded hologram, the coupling efficiency was improved to about 15%-17% over the operating temperature range. The other methods described above may not be practical for this application due to one or more of the following reasons: low efficiency, high cost, or large volume.
Thus, there is a continued need for achromatic optical systems and achromatic DOEs with high diffraction efficiency for various practical commercial applications.